But without engine game is not a game... How can engine be generic.
Engine must be made for a game... Unknown is unknown, game has the engine but we hell know nothing about it. Like Custom Built is not enough, damn it.
This and Custom built should not be rated...

Well, game engine is not like car's engine. The term "game engine" means a reusable component of a game. So if your game has no part intended for being re-used in other games, your game does not actually have an engine... Have you ever heard about tetris game engine, huh? :P